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KATSUDA Atsushi  勝田 篤

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… Alternative Names

勝田 篤  カツダ アツシ

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Researcher Number 60183779
Other IDs
External Links
Affiliation (Current) 2022: 九州大学, 数理学研究院, 教授
Affiliation (based on the past Project Information) *help 2018 – 2021: 九州大学, 数理学研究院, 教授
2012: 九州大学, 数理(科)学研究科(研究院), 教授
2012: 九州大学, 数理学研究院, 教授
2010 – 2011: 九州大学, 大学院・数理学研究院, 教授
2007 – 2009: Okayama University, Grad. School of Nat. Sci. Tech, Assoc. Prof … More
2007: Okayama University, Graduate School of Natural Science and Technology, Associate Professor
2006 – 2007: 岡山大学, 理学部, 准教授
2005 – 2006: OKAYAMA UNIVERSITY, Department of Mathematics, Associate Professor, 大学院・自然科学研究科, 助教授
2005 – 2006: 岡山大学, 大学院自然科学研究科, 助教授
1996 – 2006: 岡山大学, 理学部, 助教授
2001: Okayama University, Faculty of Science, Associate Professor, 理学部, 助教授
1993 – 1994: 岡山大学, 理学部, 助教授
1990: 岡山大学, 理学部, 助教授
1988: 岡山大学, 理学部, 助教授 Less
Review Section/Research Field
Principal Investigator
Geometry / Geometry / Basic Section 11020:Geometry-related
Except Principal Investigator
Geometry / Geometry / 代数学・幾何学 / Global analysis / Basic analysis / Global analysis / Basic analysis / Algebra / 解析学 / Algebra
Keywords
Principal Investigator
逆問題 / スペクトル / 安定性 / スペクトル逆問題 / 熱核 / inverse problem / グラフのラプラシアン / ラプラシアン / 双曲力学系 / 密度定理 … More / 境界距離 / stability / 酔歩 / ハイゼンベルグ群 / 半古典近似 / 特異摂動 / Yamabe型方程式 / 算術級数定理 / スペクトル収束 / グロモフ-ハウスドルフ距離 / 距離関数 / 閉軌道 / 負曲率多様体 / 閉測地線 / グロモフハウドルフ距離 / ハウスドルフ距離 / 等スペクトルグラフ / 等周定数 / spectrum / the Hausdorff distance / Laplacian / isospectral graphs / isoperimetric constants / ランダムウォーク / べき零群 / グロモフハウスドルフ収束 / ハーパー作用素 / random walks / nilpotent groups / Inverse spectral Problem / Gromov-Hausdorff convergence / べき零 / random walk / heat kernel / nilpotent / spectre / boundary distance / 漸近挙動 / 素閉測地線 / リッチ曲率 / キリングベクトル場 … More
Except Principal Investigator
リーマン多様体 / 測地線 / Aharonov-Bohm effect / アハラノフ・ボーム効果 / 散乱振幅 / 曲率 / 磁場散乱 / 可積分測地流 / 楕円体 / 共役跡 / リウヴィル多様体 / カットローカス / Riemannian manifolds / Dirac operator / Pauli operator / scattering by magnetic field / integrated semigroup / 比較定理 / リーマン面の被覆 / タイヒミュラー空間 / 組紐群 / 写像類群 / 散乱理論 / シュレディンガー作用素 / スペクトル理論 / cut locus / conjugate locus / ellipsoid / 閉測地線 / パウリ作用素 / scattering by magnetic fields / 磁場をもつシュレディンガー作用素 / 磁場による散乱 / resolvent convergence / P-調和写像 / グラフ / スペクトル / graph / 距離関数 / Distance functions / magnetic scattering / regularized semigroup / リプシッツ作用素半群 / resonance at zero energy / Liouville manifold / Integrable geodesic flow / semigroup of Lipschitz operators / subtangential condition / dissipativity condition / 計量構造 / 位相構造 / 幾何学不等式 / 比較定理とその応用 / リ-マン幾何学 / 同変ホモトピー論 / 分類空間 / K理論 / コンフィグレーション空間 / 一般ホモロジー理論 / グロタンディーク・デッサン / 定義体 / モジュラー関数 / ベリー関数 / 逆問題 / ディリクレ・ノイマン写像 / EIT / S行列 / 散乱行列 / 双曲計量 / シュレーディンガー方程式 / 双曲幾何学 / 関数方程式の大域理論 / スペクトル散乱理論 / 準古典漸近解析 / アハラノフ・ポーム効果 / 散乱全断面積 / 散乱位相 / 準古典近似 / ソレノイド磁場 / 準古典漸近公式 / 指数積近似 / 熱核 / 最小跡 / 半古典近似 / Liouville多様体 / Hermite-Liouville様体 / Kaehler-Liouville / Staeckel / 基本群 / ラプラシアン / L関数 / リッチ曲率 / コホモロジー / 同境理論 / 作用素 / A(p)構造 / ホモトピー型 / 等周不等式 / 等長変換群 / 多様体 / 微分幾何学的量 / 位相的性質 / 作用 / 局所等質空間 / 双曲型 / ねじれ積 / 捩れ積 / Curvature / Geodesic / Comparison Theorem / Warped product / Dirac作用素 / スピン構造 / 等スペクトル問題 / 球面空間形 / スペクトラルゼータ関数 / グラフのラプラシアン / Spin structure / isospectral problem / spherical space forms / spectral zeta functions / Laplacian for graphs / 指数積公式 / シュレディンガー半群 / 固有値漸近分布 / レゾルベント / 固有値分布 / 非一様磁場 / exponential product formula / Schrodinger semigroup / asymptotic distribution of eigenvalues / scattering amplitudes / レゾルベント収束 / デルタ型磁場 / アハロノフ・ボウム効果 / magnetic Schrodinger operator / scattering at low energy / point interaction / P-ラプラス作用素 / 無限グラフ / グリーン核 / P-harmonic morphism / P-ラプラシアン / 第1固有値 / スペクトラム / P-harmonic map / P-Laplace operator / spectrum / アレキサンドロフ空間 / 計量不変量 / Alexandrov spaces / Curvatures / Metric Invariants / デルタ磁場 / point-like magneticfield / scattreing amplitude / scattering amplitude / magnetic vortex / Aharonov-Bohm efrect / magnetic Scchrodinger operator / δ-like magnetic field / scattering arnplitude / 遠アーベル幾何 / 外ガロア表現 / 絶対ガロア群 / グロタンディーク予想 / グロタンデイーク予想 / anabelian geometry / outer Galois representation / Teichmueller space / mapping class group / braid group / absolute Galois group / Grothendieck Conjecture / covers of Riemann surfaces / 抽象的準線形発展方程式 / Hadamardの意味の適切性 / 安定性 / 保存則系 / 無限小生成作用素 / semigroup of Lipschite operators / infinitesimal generators / generation theorem / conservation laws / Templ type / Riemann problem / wave front tracking solution / abstract quasi-linear equation / Hadamard well-posedness / stability / conservation law / generator / Lipschitz semigroup / ディラック作用素 / 零エネルギーレゾナンス / Dirac operators / Pauli operators / Feynman-Kac formula / zero energy resonance / Trotter-Kato product formula / Aharonov-Bohm field / point-like magnetic field / spectral theory / ヤコビ / 楕円面 / 2次曲面 / 共役蹠 / リウヴィル曲面 / 極 / 射影同値 / 双曲面 / Jacobi / tri-axial ellipsoid / quadratic surface / 発展方程式 / アダマールの意味の適切性 / 劣接線条件 / 消散条件 / 安定性条件 / 作用素半群の近似定理 / semigroup of operators / semilinear equation / quasilinear equation / Hadamard wellposedness / perturbation / analytic semigroup / fractional power / metric-like functional / Chernoff's product formula / quasilinear evolution equation / semilinear evolution equation / acoustic boundary condition / Wentzell boundary condition / non-densely defined operator / well-posedness / semigroup of lipschitz operators / comparison function / infinitesimal generator / abstract Cauchy problem / evolution equation / wellposedness in the sense of Hadamard / stability condition / approximation theorem for semigroups of operators / p-調和写像 / p-調和関数 / 幾何学 / p-ラプラシアン / p-harmonic morphism / p-harmonic function / p-harmonic map / Riemannian manifold / モース理論 / 切断跡 / Morse theory / Geodesics / Cut loci / 可積化測地流 / カスプ / ケーラー・リウヴィル多様体 / エルミート・リウヴィル多様化 / Ellipsoid / Cut locus / Conjugate locus / Cusp / Kahler-Liouville / Hermite-Liouville Less
  • Research Projects

    (33 results)
  • Research Products

    (49 results)
  • Co-Researchers

    (61 People)
  •  Density Theorems of Closed Geodesics for Nilpotent Extensions and Asymptotics of Heat KernelsPrincipal Investigator

    • Principal Investigator
      勝田 篤
    • Project Period (FY)
      2018 – 2022
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 11020:Geometry-related
    • Research Institution
      Kyushu University
  •  Structures of manifolds and asymptoticpropertiesPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2010 – 2012
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Kyushu University
  •  Development of various problems related to integrable geodesic flows

    • Principal Investigator
      KIYOHARA Kazuyoshi
    • Project Period (FY)
      2008 – 2010
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  Geometric Structures and TopologyPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2007 – 2009
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  Development of numerical computation brought by spectral theory and geometry

    • Principal Investigator
      ISOZAKI Hiroshi
    • Project Period (FY)
      2006 – 2008
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Basic analysis
    • Research Institution
      University of Tsukuba
  •  Asymptotic Analysis in Spectral and Scattering Theory

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      2006 – 2008
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Global analysis
    • Research Institution
      Okayama University
  •  Problems related to integrable geodesic flows

    • Principal Investigator
      KIYOHARA Kazuyoshi
    • Project Period (FY)
      2006 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  Metric invariants and space structures

    • Principal Investigator
      SAKAI Takashi
    • Project Period (FY)
      2005 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University of Science
  •  モジュライ空間の算術幾何に対する種種のグラフ複合体の関与の研究

    • Principal Investigator
      NAKAMURA Hiroaki
    • Project Period (FY)
      2004 – 2005
    • Research Category
      Grant-in-Aid for Exploratory Research
    • Research Field
      Algebra
    • Research Institution
      Okayama University
  •  Relations of geometric structure of manifolds and graphs, spectre, asymptotic analysis and their applicationsPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2004 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Integrable geodesic flows and related problems

    • Principal Investigator
      KIYOHARA Kazuyoshi
    • Project Period (FY)
      2004 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  Wellposedness of the Cauchy problems for hyperbolic systems with large data

    • Principal Investigator
      TANAKA Naoki
    • Project Period (FY)
      2004 – 2006
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      Shizuoka University
      Okayama University
  •  studies on the relationship of the structure of manifolds and p-harmonic functions

    • Principal Investigator
      TAKEUCHI Hiroshi
    • Project Period (FY)
      2004 – 2007
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Global analysis
    • Research Institution
      Shikoku University
  •  Scattering of Dirac particles by mabnetic fields and spectral theory

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      2003 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Global analysis
    • Research Institution
      Okayama University
  •  Galois groups and fundamental groups in anabelian geometry

    • Principal Investigator
      NAKAMURA Hiroaki
    • Project Period (FY)
      2002 – 2005
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Algebra
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Spectra and Geometric structure of manifolds and graphPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2002 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Well-posedness and approximation of Cauchy problems for hyperbolic systems

    • Principal Investigator
      TANAKA Naoki
    • Project Period (FY)
      2002 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Scattering by magnetic fields and Aharonov-Bohm effect

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      2001 – 2002
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Basic analysis
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Relations between space-structures and curvatures

    • Principal Investigator
      SAKAI Takashi
    • Project Period (FY)
      2000 – 2003
    • Research Category
      Grant-in-Aid for Scientific Research (B)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Geometric Structures on Manifolds and GraphsPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      2000 – 2001
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Spectral Theory for Schrodinger Operators with Magnetic Fields and its Application

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      1999 – 2000
    • Research Category
      Grant-in-Aid for Scientific Research (B).
    • Research Field
      Global analysis
    • Research Institution
      Okayama University
  •  The properties of P-harmonic maps and the application to Geometry

    • Principal Investigator
      TAKEUCHI Hiroshi
    • Project Period (FY)
      1999 – 2001
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Global analysis
    • Research Institution
      Shikoku University
  •  Geometric structure and topology of manifolds and graphsPrincipal Investigator

    • Principal Investigator
      KATSUDA Atsushi
    • Project Period (FY)
      1998 – 1999
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  CURVATURE AND STRUCURE OF SPACES

    • Principal Investigator
      SAKAI Takashi
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  SPECTRAL GEOMETRY

    • Principal Investigator
      IKEDA Akira
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      OKAYAMA UNIVERSITY
  •  Spectral and Scattering Theory and its Application

    • Principal Investigator
      TAMURA Hideo
    • Project Period (FY)
      1997 – 1998
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      解析学
    • Research Institution
      Okayama University
      Ibaraki University
  •  計量構造と多様体構造

    • Principal Investigator
      酒井 隆
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  多様体の幾何構造と位相Principal Investigator

    • Principal Investigator
      勝田 篤
    • Project Period (FY)
      1996
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  同変ホモトピー論とその応用

    • Principal Investigator
      SHIMAKAWA Kazuhisa
    • Project Period (FY)
      1994
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  双曲力学系及び非線型偏微分方程式Principal Investigator

    • Principal Investigator
      勝田 篤
    • Project Period (FY)
      1993
    • Research Category
      Grant-in-Aid for Encouragement of Young Scientists (A)
    • Research Field
      Geometry
    • Research Institution
      Okayama University
  •  計量構造と位相構造

    • Principal Investigator
      SAKAI Takashi
    • Project Period (FY)
      1990
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Okayama University
  •  曲面論と多様体論の微分幾何学的研究

    • Principal Investigator
      森本 明彦
    • Project Period (FY)
      1988
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Nagoya University
  •  一般コホモロジー論

    • Principal Investigator
      藤井 道一
    • Project Period (FY)
      1988
    • Research Category
      Grant-in-Aid for General Scientific Research (C)
    • Research Field
      代数学・幾何学
    • Research Institution
      Okayama University

All 2022 2021 2020 2019 2013 2012 2011 2009 2007 2006 2005 2004

All Journal Article Presentation Book

  • [Book] Closed geodesics and heat kernels on nilpotent coverings2011

    • Author(s)
      A.Katsuda
    • Publisher
      Geometry and Something
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Journal Article] An extension of the Bloch-Floquet theory to the Heisenberg group and its applications to asymptotic problems for heat kernels and prime closed geodesics2022

    • Author(s)
      勝田 篤
    • Journal Title

      数理解析研究所講究禄

      Volume: 2201 Pages: 59-75

    • NAID

      120007170963

    • Open Access
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Journal Article] A rigidity theorem for Killing vector fields on compact manifolds with almost nonpositive Ricci curvature2021

    • Author(s)
      Katsuda, Atsushi; Nakamura, Takuya
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 149 Pages: 1215-1224

    • DOI

      10.1090/proc/14742

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Journal Article] An Overview of Sunada's work up to age 602009

    • Author(s)
      Atsushi Katsuda
    • Journal Title

      Contemporary Mathematics 484

      Pages: 7-42

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Journal Article] An overview of Sunada's work up to age 602009

    • Author(s)
      A. Katsuda, P.W. Sy
    • Journal Title

      Contemp. Math. 484

      Pages: 7-42

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Probl.Imaging 1・1

      Pages: 135-157

    • Data Source
      KAKENHI-PROJECT-17540079
  • [Journal Article] Stability of boundary representation and reconstruction of Riemannian Manifolds.2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging 1

      Pages: 135-157

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M. Lassas
    • Journal Title

      Inverse Problems and Imaging 1-1

      Pages: 135-157

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Journal Article] Stability of boundary distance and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M. Lassas
    • Journal Title

      Inverse Prob. Imaging 1

      Pages: 135-157

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M. Lassas
    • Journal Title

      Inverse Problems and Imaging 1

      Pages: 135-157

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging 1

      Pages: 135-157

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. kurylev, M. Lassas
    • Journal Title

      Inverse Problems and Imaging

      Pages: 135-157

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Journal Article] Stability of boundary representation and reconstruct ion of Riemannian Manifolds.2007

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging. 1

      Pages: 135-157

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Matti ; Stability of boundary distance representation and reconstruction of Riemannian manifolds2007

    • Author(s)
      A. Katsuda, Y. Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging 1 no. 1

      Pages: 135-157

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-18340034
  • [Journal Article] Stability of boundary distance representation and reconstruction of Riemannian manifolds2006

    • Author(s)
      A.Katsuda, Y.Kurylev, M.Lassas
    • Journal Title

      Inverse Problems and Imaging Vol 1, No 1

      Pages: 135-157

    • Data Source
      KAKENHI-PROJECT-18340034
  • [Journal Article] Boundary regularity for the Ricci equation, geometric convergence, and Gelfand's inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda 他(計5名)
    • Journal Title

      Invent.Math. 158

      Pages: 261-321

    • Data Source
      KAKENHI-PROJECT-16540069
  • [Journal Article] Boundary regularity for the Ricci equation, geometric convergence, and Gel' fand inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda 他3名
    • Journal Title

      Invent. Math. 158

      Pages: 261-321

    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Boundary regularity for the Ricci equat ion, geometric convergence, and Gel' fand inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda et al.
    • Journal Title

      Invent. Math. 158

      Pages: 261-321

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Boundary regularity for Ricci equation,geometric convergence,and Gel'fand's inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda, et. al.
    • Journal Title

      Invent.Math. 158

      Pages: 261-321

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-16540208
  • [Journal Article] Boundary regularity for the Ricci equation, geometric convergence, and Gel' fand inverse boundary problem2004

    • Author(s)
      M.Anderson, A.Katsuda 他3名
    • Journal Title

      Invent.Math. 158

      Pages: 261-321

    • Data Source
      KAKENHI-PROJECT-16540068
  • [Journal Article] Boundary regularity for Ricci equation, geometori Convergence, and Gel'fand's inverse boundary problem2004

    • Author(s)
      M. Anderson, A. Katsuda, Y. Kurylev, M. Lassas, M. Taylor
    • Journal Title

      Invent. Math. 158

      Pages: 261-321

    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-16540208
  • [Presentation] Nash の埋め込み定理の原証明とその応用可能性2022

    • Author(s)
      勝田 篤
    • Organizer
      研究集会「測地線及び関連する諸問題」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] Riemann の教授資格取得講演と現代のリーマン幾何学2022

    • Author(s)
      勝田 篤
    • Organizer
      研究会「直観幾何学 2022」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] 素数と素閉測地線ーDirichlet,Riemann,Selbergー2022

    • Author(s)
      勝田 篤
    • Organizer
      研究会「直観幾何学 2022」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] 閉測地線, 熱核, ハイゼンベルグ群2020

    • Author(s)
      勝田 篤
    • Organizer
      研究集会「測地線及び関連する諸問題」
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] Closed geodesics and heat kernels for Heisenberg extensions2019

    • Author(s)
      勝田 篤
    • Organizer
      研究集会「 多様体上の微分方程式 」金沢シリーズ第18回
    • Invited
    • Data Source
      KAKENHI-PROJECT-18K03282
  • [Presentation] Toward a geometric density theorem for nilpotent extensions2013

    • Author(s)
      A. Katsuda
    • Organizer
      Low dimensional topology and number theory V
    • Place of Presentation
      福岡ソフトリサーチパーク
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] ハイゼンベルグ群に対する幾何学的密度定理に向けて2013

    • Author(s)
      勝田 篤
    • Organizer
      小研究会「測地線及び関連する諸問題」
    • Place of Presentation
      熊本大学
    • Invited
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Toward a geometric dennsity theorem for nilpotent extensions2013

    • Author(s)
      Atsushi Katsuda
    • Organizer
      Low dimennsional topology and number theory V
    • Place of Presentation
      Fukuoka,
    • Invited
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] ハイゼンベルグ群に対する幾何学的密度定理に向けて2013

    • Author(s)
      勝田 篤
    • Organizer
      研究集会 測地線及び関連する諸問題
    • Place of Presentation
      熊本大学
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Closed geodesics and heat kernels on nilpotent coverings2012

    • Author(s)
      勝田 篤
    • Organizer
      研究集会 測地線及び関連する諸問題
    • Place of Presentation
      熊本大学
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Closed geodesics and heat kernels on nilpotent coverings2012

    • Author(s)
      勝田篤
    • Organizer
      研究集会「測地線及び関連する諸問題」
    • Place of Presentation
      熊本大学(招待講演)
    • Year and Date
      2012-01-09
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] 境界付多様体の境界距離表現と内部距離2011

    • Author(s)
      勝田 篤
    • Organizer
      研究集会 測地線及び関連する諸問題
    • Place of Presentation
      熊本大学
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Density theorems of closed geodesics for nilpotent extensions2011

    • Author(s)
      勝田篤
    • Organizer
      Geometry and Something
    • Place of Presentation
      福岡大学(招待講演)
    • Year and Date
      2011-11-03
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] 境界付多様体の境界距離表現と内部距離2011

    • Author(s)
      勝田篤
    • Organizer
      研究集会「測地線及び関連する諸問題」
    • Place of Presentation
      熊本大学(熊本)
    • Year and Date
      2011-01-08
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] Density theorems of closed geodesics for nilpotent extensions2011

    • Author(s)
      勝田 篤
    • Organizer
      福岡大学微分幾何学研究会
    • Place of Presentation
      福岡大学
    • Data Source
      KAKENHI-PROJECT-22540086
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      A. Katsuda
    • Organizer
      Spectral Analysis in Geometry and Number Theory
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-08-07
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      A. Katsuda
    • Organizer
      Spectral Analysis in Geometry and Number Theory
    • Place of Presentation
      Nagoya Univ
    • Year and Date
      2007-08-07
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Spectral analysis in geometry2007

    • Author(s)
      勝田篤
    • Organizer
      岡山幾何学談話会
    • Place of Presentation
      岡山大学
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      勝田 篤
    • Organizer
      Spectral Analysis in Geometry and Number theory
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-08-07
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Spectral Analysis in Geometry2007

    • Author(s)
      A. Katsuda
    • Organizer
      Okayama Colloquium on Geometry
    • Place of Presentation
      Okayama Univ
    • Year and Date
      2007-07-27
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Spectral Analysis in Geometry2007

    • Author(s)
      勝田 篤
    • Organizer
      第17回岡山幾何学談話会
    • Place of Presentation
      岡山大学
    • Year and Date
      2007-07-27
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] An overview of Sunada's works2007

    • Author(s)
      勝田篤
    • Organizer
      International Symposium“Spectral Analysis in Geometry and Number Theory"
    • Place of Presentation
      名古屋大学
    • Data Source
      KAKENHI-PROJECT-19540088
  • [Presentation] On the stability of Gel'fand inverse spectral problem2005

    • Author(s)
      A. Katsuda
    • Organizer
      Spectral Analysis, Global Analysis and PDE 2005
    • Place of Presentation
      Keio Univ
    • Year and Date
      2005-05-13
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] On the stability of the Gel'fand inverse spectral problem2005

    • Author(s)
      勝田 篤
    • Organizer
      Spectral Analysis, Global Analysis and PDE 2005
    • Place of Presentation
      慶応義塾大学
    • Year and Date
      2005-05-13
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Gel'fandのスペクトル逆問題の安定性について2005

    • Author(s)
      勝田 篤
    • Organizer
      日本数学会年会幾何学分科会特別講演
    • Place of Presentation
      日本大学
    • Year and Date
      2005-03-30
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] On the stability of Gel'fand inverse spectral problem2005

    • Author(s)
      A. Katsuda
    • Organizer
      Tohoku Geometry Seminar
    • Place of Presentation
      Tohoku Univ
    • Year and Date
      2005-06-28
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] Gel'fandのスペクトル逆問題の安定性について2005

    • Author(s)
      勝田 篤
    • Organizer
      東北大学幾何セミナー
    • Place of Presentation
      東北大学
    • Year and Date
      2005-06-28
    • Description
      「研究成果報告書概要(和文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • [Presentation] On the stability of Gel'fand inverse spectral problem2005

    • Author(s)
      A. Katsuda
    • Organizer
      Special lecture at annual meeting of Math. Soc. Japan
    • Place of Presentation
      Nihon Univ
    • Year and Date
      2005-03-30
    • Description
      「研究成果報告書概要(欧文)」より
    • Data Source
      KAKENHI-PROJECT-17540079
  • 1.  SAKAI Takashi (70005809)
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  • 2.  TAMURA Hideo (30022734)
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